Analytical & Problem-Solving Skills

Data Sufficiency 

Learning Outcome

Recall / Revisit

Think About It

When solving a problem:

• Do we always need the exact answer?

• Is it enough to know whether the answer can be determined?

Data Sufficiency Focus

Not finding the answer.

Finding whether enough information exists.

Why is Data Sufficiency Important?

Develop Critical Thinking Skills

Improve Information Evaluation Ability

Strengthen Logical Decision-Making

Frequently Asked in Placement Assessments

What is Data Sufficiency?

Data Sufficiency is a type of reasoning question where you are not asked to find the actual answer.

Instead, you must decide:

"Do I have enough information to answer the question?"

The focus is on whether the given data is sufficient, not on solving the problem completely.

Here are a few Data Sufficiency examples

from different topics with step-by-step analysis.

Age Problem

Question :-

What is Rahul's age?

Statement I:

Rahul is 5 years older than Amit.

Statement II:

Amit is 12 years old.

Age Problem

Statement I alone

Rahul = Amit + 5

But Amit's age is unknown.

Statement II alone

Amit = 12

But Rahul's age is unknown.

Both together

Rahul = 12 + 5 = 17

Analysis:

Not sufficient

Not sufficient

Sufficient

Answer:- Option C – Both statements together are sufficient.

Linear Equation

Question :-

Is the number N even?

Statement I:

N is divisible by 2.

Statement II:

N is divisible by 6.

Linear Equation

Analysis:

Answer:- Option D – Either statement alone is sufficient.

Statement I alone

Any number divisible by 2 is even.

Sufficient

Statement II alone

Any number divisible by 6 is also divisible by 2.

Sufficient

Number System

Question :-

What is x?

Statement I:

x+8=20x + 8 = 20x+8=20

Statement II:

2x=242x = 242x=24

Number System

Analysis:

Answer:- Option D – Either statement alone is sufficient.

Statement I alone

Statement II alone

x=12x = 12x=12

x=12x = 12x=12

Types of Arrangements

Linear Arrangement

Example

• A sits opposite B.

• C sits to the immediate right of A.

• D sits between B and E.

Find everyone's position.

Since there is no fixed start or end, these require careful direction tracking.

People sit around a square or rectangular table.

Questions may involve:

• Corners

• Sides

• Facing inside or outside

Rectangular/Square Arrangement

Types of Arrangements

Circular Arrangement

People sit around a table in a circle.

Example

• A sits opposite B.

• C sits to the immediate right of A.

• D sits between B and E.

Find everyone's position.

Since there is no fixed start or end, these require careful direction tracking.

What are Puzzles and Arrangements

What are Puzzles?

A puzzle contains multiple pieces of information that must be connected logically.

Unlike arrangements, puzzles often involve several categories.

Example Puzzle :-

Five friends:

Each likes a different fruit:

What are Puzzles and Arrangements

Clues:

1

2

3

A likes Apple.

B does not like Mango.

The person who likes Orange sits next to C.

Solution

This is called a Logic Puzzle.

Types of Puzzles

Recall

Before We Begin...

Answer the following:

1

3

2

What is meant by a "constraint" in a puzzle?

How many neighbours does a person have in a circular arrangement?

Which is easier to solve first:

OR

A constraint is a rule or condition given in the puzzle that limits the possibilities and helps us find the solution.

A person has 2 neighbours in a circular arrangement -one on the left and one on the right.

Direct clues

Indirect clues

Clues that give clear and direct information.

Clues that need some other information to be understood.

Key Concepts

1

Read all clues carefully.

2

Start with definite information.

3

Use diagrams and tables.

4

Eliminate impossible positions.

5

Verify all clues before finalizing.

Linear Arrangement

People or objects are arranged in a straight line.

Common term

Immediate Left

Immediate Right

Second to the Left

Extreme Ends

Facing North/South

Strategy

1

2

3

4

Draw blank positions.

Place fixed positions first.

Use elimination.

Check all conditions.

Linear Arrangement

Examples:-

Five friends A, B, C, D, and E are sitting in a row.

• A sits at one end.

• C sits in the middle.

• B sits immediately right of A.

• E sits at the other end.

Find the arrangement.

Solutions

Positions:- 

1

2

3

4

A

B

C

D

1

2

3

4

A at one end

B immediately right of A → Position 2

C in middle → Position 3

E at other end → Position 5

D occupies remaining position.

Solutions

A  -  B  -  C  -  D  -  E

Linear Arrangement

Problem:-

Six people P, Q, R, S, T, U sit in a row.

• P sits left of Q.

• R sits at an end.

• T sits between P and Q.

• U sits rightmost.

Find possible arrangement.

Remaining arrangement:

Solution:-

Circular Arrangement

People sit around a circle.

Important Rule:

Everyone has exactly two neighbors.

Relative positions matter.

Fix one person to avoid rotation confusion.

Circular Arrangement

Problem:-

Four friends A, B, C, D sit around a circular table.

• A sits opposite C.

• B sits right of A.

Who sits left of A?

Fix A.

B sits right of A.

Remaining seat occupied by D.

C opposite A.

Circular Arrangement

Problem:-

Five people sit around a circle.

• P is between Q and R.

• S sits opposite P.

• T sits next to S.

Determine arrangement.

Fix P.

Place Q and R adjacent.

S opposite P.

Final Agreement:-

T next to S.

Logical Puzzle Solving

Steps to Solve Any Puzzle

1

Read all clues.

2

Identify direct clues.

3

Create table/diagram

4

Mark confirmed positions.

5

Eliminate impossible options.

6

Cross-check all clues.

Logical Puzzle

Problem

Three employees—Aman, Bharat, and Charan —work in HR, IT, and Finance.

• Aman is not in HR.

• Bharat is not in Finance.

• Charan works in IT.

Who works in Finance?

Solution

Logical Puzzle

Problem

Answer

Aman works in Finance.

Analytical Puzzle

Problem

Solution

• Three boxes are labeled:

• All labels are incorrect.​

• You may pick one fruit from one box only.

• How will you correctly label all boxes?

Logical Puzzle

1

Pick fruit from box labeled "Mixed".

2

Since all labels are wrong:

If fruit is Apple,

3

Use elimination to label remaining boxes.

Solution

Practice Questions

Solution

Five students A, B, C, D, E sit in a row.

• A sits left of B.

• C sits at one end.

• D sits between A and B.

Find arrangement.

Six people sit in a line.

• P sits at left end.

• Q sits immediately right of P.

• R sits in middle.

• T sits at right end.

Arrange them.

Q 1.

Q 2.

Practice Questions

Solution

Four friends sit around a circle.

• A opposite B.

• C sits right of A.

Who sits left of B?

Five people sit around a circular table.

• P between Q and R.

• S opposite Q.

• T next to P.

Determine arrangement.

Q 3.

Q 4.

Practice Questions

Solution

Three children—A, B, C—have Red, Blue, and Green bags.

• A does not have Red.

• B has Green.

Who has Blue?

Six employees sit in a row.

• M sits at one end.

• N sits immediately left of O.

• P sits in middle.

• Q sits rightmost.

Find arrangement.

Q 5.

Q 6.

Key Takeaway

• Start with direct clues

• Draw diagrams and tables

• Use elimination techniques

• Fix one position in circular arrangements

• Verify every clue before finalizing

• Practice improves speed and accuracy

Summary

Q1. What is the value of x?

Statement I: x = 15

Statement II: x is greater than 10

Q1. What is the value of x?

Statement I: x = 15

Statement II: x is greater than 10